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Calculus problem

  1. Nov 6, 2008 #1
    1. The problem statement, all variables and given/known data
    show f(x)=x^3-3x^2+2x is not one to one on (-infinity,+infinity)


    2. Relevant equations

    finding the largest value of k such as f is one to one on interval (-k,k)
    3. The attempt at a solution
    i can get f`(x)=3x^2-6x+2 but it is positive so f(x) should be one-to-one
    how to prove it
     
  2. jcsd
  3. Nov 6, 2008 #2

    Dick

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    f(x)=3x^2-6x+2 isn't positive. f(1)=-1.
     
    Last edited by a moderator: Nov 7, 2008
  4. Nov 7, 2008 #3

    HallsofIvy

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    I just automatically looked at the discrimant for 3x2- 6x+ 2:
    [tex]\sqrt{6^2- 4(3)(2)}= \sqrt{36- 24}= \sqrt{12}[/tex]
    Since that is a real number, the 3x2- 6x+2 changes sign, and the original function changes "direction", at two places.
     
  5. Nov 7, 2008 #4
    thanks but how can i do this
    largest value of k such as f is one to one on interval (-k,k)
     
  6. Nov 7, 2008 #5

    HallsofIvy

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    A function f(x) is one-to-one as long as its derivative does not change sign- and a continuous derivative, such as the derivative of any polynomial, can change sign only where the derivative is 0.

    Solve 3x2- 6x+ 2= 0, say by using the quadratic formula. Those 2 values will give 3 intervals on which the function is one to one. One of them contains the an interval of the form (-k, k).
     
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